This effectively means that we use another prolongation of the distance 
function on M into the surrounding space.  Since the prolongation does not
matter this patch should not change the algorithm behavior.  However, it
shaves off a few norm calculations and division.  I cannot really measure
any difference though.

A possible effect of this is that while all values should remain on the
manifold, they may start to 'drift away' due to numerical artifacts.
So we may have to add an occasional renormalization step eventually.

[[Imported from SVN: r9558]]

When using the classes with ADOL-C, T becomes an 'adouble',
which is a non-trivial type.  However, the convexityField
is constexpr (and with a reason -- otherwise we could write
the initialization together with the declaration), and
constexpr and non-trivial types don't work together.

[[Imported from SVN: r9444]]

Because ADOL-C doesn't like calls to sqrt(0), obviously.
The use of sqrt(x) for small x can be avoided completely
using modified series expansions, because the overall
function exp is differentiable even at x=0.

[[Imported from SVN: r9426]]

Makes for a more precise Hessian matrix when using automatic differentiation.

[[Imported from SVN: r9425]]

[[Imported from SVN: r9424]]

Because ADOL-C cannot handle the latter

[[Imported from SVN: r9386]]

[[Imported from SVN: r9385]]

[[Imported from SVN: r9384]]

And use it in the test.

This patch uses the new 'constexpr' macro.  Hence it is C++11 only.

[[Imported from SVN: r9195]]

[[Imported from SVN: r8972]]

with respect to the quaternion coordinates.  Or, in other words,
the second derivative of the map from quaternions to 
orthogonal matrices.

[[Imported from SVN: r8407]]

New implementation properly handles the two sheets.

Now the TargetSpace test passes again.  Yay!

[[Imported from SVN: r8375]]

The new implementation should take proper care of the two-sheet structure.

I am writing 'should' here: it still fails the test sometimes,
but then the result appears to be close enough to think rounding errors
are responsible.

[[Imported from SVN: r8373]]

The new implementation properly handles the double-sheet structure

[[Imported from SVN: r8372]]

don't keep a private implementation of derivativeOfArcCosSquared -- use the one from UnitVector instead

[[Imported from SVN: r8371]]

Properly taking into account the two-sheet covering structure

[[Imported from SVN: r8370]]

[[Imported from SVN: r8368]]

Now it properly handles the situation that p and q may be on
different sheets of the double cover.

[[Imported from SVN: r8367]]

[[Imported from SVN: r8366]]

This is safer, because calling the constructor implicitly
can lead to unwanted quaternion normalization.
(happened to me...)

[[Imported from SVN: r8344]]

Even though multiplication of Rotations is the same thing
as multiplication of Quaternions, in the first case the
output is a Rotation class, and in the second on a Quaternion
class.

[[Imported from SVN: r8343]]

[[Imported from SVN: r8342]]

[[Imported from SVN: r8333]]

[[Imported from SVN: r8329]]

Quaternion class to the Rotation class.  Rotation axes and
angles are a genuine rotation concept and don't really
belong into a quaternion implementation.

[[Imported from SVN: r8207]]

It makes it difficult to be sure that an explicitly
requested type is really handed over to every place.

While we are at it: reverse the order of the template
parameters.  Now first comes the type, then the dimension.
This is more like FieldVector and friends, and hence
should be less confusing.

[[Imported from SVN: r8148]]

[[Imported from SVN: r8146]]

[[Imported from SVN: r8115]]

[[Imported from SVN: r8111]]

[[Imported from SVN: r8110]]

[[Imported from SVN: r8105]]

[[Imported from SVN: r8104]]

fix interpolation-bug when quaternions don't have the same sign. Thanks to Oliver Sander for the patch ;-)

[[Imported from SVN: r8102]]

[[Imported from SVN: r8101]]

[[Imported from SVN: r8058]]

[[Imported from SVN: r8034]]

[[Imported from SVN: r8020]]

[[Imported from SVN: r8010]]

[[Imported from SVN: r8009]]

[[Imported from SVN: r8005]]